The idea of a quotient group follows easily from cosets and Lagrange's theorem. In this video, we start with a normal subgroup and develop the idea of a quotient group, by viewing each coset (together with the normal subgroup) as individual mathematical objects in a set. This set, under
From playlist Abstract algebra
Now that we know what a quotient group is, let's take a look at an example to cement our understanding of the concepts involved.
From playlist Abstract algebra
We give a buttload of definitions for morphisms on various categories of complexes. The derived category of an abelian category is a category whose objects are cochain complexes and whose morphisms I describe in this video.
From playlist Derived Categories
Chapter 5: Quotient groups | Essence of Group Theory
Quotient groups is a very important concept in group theory, because it has paramount importance in group homomorphisms (connection with the isomorphism theorem(s)). With this video series, abstract algebra needs not be abstract - one can easily develop intuitions for group theory! In fac
From playlist Essence of Group Theory
Abstract Algebra | Quotient Groups
We introduce the notion of a quotient group and give some examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
Now that we know what quotient groups, a kernel, and normal subgroups are, we can look at the first isomorphism theorem. It states that the quotient group created by the kernel of a homomorphism is isomorphic to the (second) group in the homomorphism.
From playlist Abstract algebra
algebraic geometry 13 Three examples of quotients
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers three examples of quotients by groups: a cyclic quotient singularity, the parameter space of cyclohexane, and the moduli space of elliptic curves. Correction: o
From playlist Algebraic geometry I: Varieties
G is Abelian if the Quotient Group G/N is cyclic and N is contained in the Center Proof
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys G is Abelian if the Quotient Group G/N is cyclic and N is contained in the Center Proof
From playlist Abstract Algebra
Fundamentals of Mathematics - Lecture 25: Quotient Maps (Real Projective Line, Modular Arithmetic)
course page - https://www.uvm.edu/~tdupuy/logic/Math52-Fall2017.html videography - Eric Melton, UVM
From playlist Fundamentals of Mathematics
Gregory Henselman-Petrusek (9/28/22): Saecular persistence
Homology with field coefficients has become a mainstay of modern TDA, thanks in part to structure theorems which decompose the corresponding persistence modules. This naturally begs the question -- what of integer coefficients? Or homotopy? We introduce saecular persistence, a categoric
From playlist AATRN 2022
A (proper) introduction to derived CATegories
While there are introductions to derived categories that are more sensible for practical aspects, in this video I give the audience of taste of what's involved in the proper, formal definition of derived categories. Special thanks to Geoff Vooys, whose notes (below) inspired this video: ht
From playlist Miscellaneous Questions
Free Group Rings by I. B. S. Passi
PROGRAM GROUP ALGEBRAS, REPRESENTATIONS AND COMPUTATION ORGANIZERS: Gurmeet Kaur Bakshi, Manoj Kumar and Pooja Singla DATE: 14 October 2019 to 23 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Determining explicit algebraic structures of semisimple group algebras is a fund
From playlist Group Algebras, Representations And Computation
On the notion of λ-connection - Carlos Simpson
Geometry and Arithmetic: 61st Birthday of Pierre Deligne Carlos Simpson University of Nice October 18, 2005 Pierre Deligne, Professor Emeritus, School of Mathematics. On the occasion of the sixty-first birthday of Pierre Deligne, the School of Mathematics will be hosting a four-day confe
From playlist Pierre Deligne 61st Birthday
Algebraic K-Theory Via Binary Complexes - Daniel Grayson
Daniel Grayson University of Illinois at Urbana-Champaign; Member, School of Mathematics October 22, 2012 Quillen's higher K-groups, defined in 1971, paved the way for motivic cohomology of algebraic varieties. Their definition as homotopy groups of combinatorially constructed topolo
From playlist Mathematics
Lecture 12: Classifying topoi (Part 1)
This is the first of several talks on the subject of classifying topoi. I began with a brief reminder of the overall picture from the first talk, i.e. what are classifying topoi and why do we care (from the point of view of organising mathematics). Then I spent some time talking about tens
From playlist Topos theory seminar
Fourier transform for Class D-modules - David Ben Zvi
Locally Symmetric Spaces Seminar Topic: Fourier transform for Class D-modules Speaker: David Ben Zvi Affiliation: University of Texas at Austin; Member, School of Mathematics Date: Febuary 13, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Francis Brown - 1/4 Mixed Modular Motives and Modular Forms for SL_2 (\Z)
In the `Esquisse d'un programme', Grothendieck proposed studying the action of the absolute Galois group upon the system of profinite fundamental groups of moduli spaces of curves of genus g with n marked points. Around 1990, Ihara, Drinfeld and Deligne independently initiated the study of
From playlist Francis Brown - Mixed Modular Motives and Modular Forms for SL_2 (\Z)
Joseph Silverman, Moduli problems and moduli spaces in algebraic dynamics
VaNTAGe seminar on June 23, 2020. License: CC-BY-NC-SA. Closed captions provided by Max Weinreich
From playlist Arithmetic dynamics
Differential Equations | Abel's Theorem
We present Abel's Theorem with a proof. http://www.michael-penn.net
From playlist Differential Equations